ERT 246
Hydrology & Water
Resources Engineering
Siti Kamariah Md Sa’at
School of Bioprocess Engineering,
UniMAP
Unit Hydrograph
Cont.
More Example:
 Two storm each of 6-hr duration and
having rainfall excess values of 3.0cm
and 2.0 cm respectively occur
successively. The 2-cm ER rain follows
the 3-cm rain. The 6-hr UH for the
catchment is the same as given in
previous example. Calculate the resulting
DRH.
Unit Hydrograph of
Different Durations



Under condition where lack of adequate data
in developement of unit hydrograph
D-hour unit hydrograph is used to develop
unit hydrographs of differing durations nD
Two method available:
1. Method of superposition
2. The S-Curve
Method of superposition
 If a D-h unit hydrograph is available, and
its desired to develop unit hydrograph of
nD, its is easily accomplished by
superposing n unit hydrographs with
each graph separated from the previous
on by D-h.
D = 2-Hr Unit Hydrograph
Adjusted Net Rainfall
one inch over basin
Qp
Change UH Duration
Consider 1 hr UH
Add and Lag two UH
by one hour
Sum and divide by 2
Results in 2 hr UH
Example
 Given the ordinates of a 4-hr unit hydrograph
as below derive the ordinates of a 12-hr unit
hydrograph for the same catchment
Time (hr)
0
4
8
12
16
20
24
28
32
36 40
44
Ordinates of
4-hr UH
0
20 80 130 150 130 90
52
27
15
0
5
Equilibrium Hydrograph
Uniform Rain
Inflow = Outflow
Equiv to summing n
hydrographs in T
One Hydrograph
Produces S curve
S-Curve
 Also known as S-hydrograph
 Hydrograph produced by continous
effective rainfall at a constant rate for
infinite period.
 Curve obtained by summation of an
infinite series of D-h UH spaced D-h
apart.
S-Curve Construction
 Obtained by adding a string of D-h UH each
lagged by D-hours from one another.
 If Tb= base period of the UH, addition of only
Tb/D UH are suffcient to obtained S-curve
 U(t) = S(t)-S(t-D) or U(t) = S(t)+S(t-D)
Where
 S(t-D)= S-curve addition at time t
 S(t) = Ordinate of D-h UH at time t
S-Curves for UH
S-Curves
S-curve
• Convert 2 hr Unit
hydrograph to 3-hr
• Lag each 2-hr UH by
Duration D
• Add to produce S-curve
Lag S Curves in time, subtract them,
and multiply by D/D’
Lag by D’ and subtract both curves
3 hr. Unit Hydrograph
from a 2 hr. UH (D/D’)
3 HR UH
Example
 Solve previous example with S-curve
method:
Hydrograph Convolution
1
2
Add and Lag Method
3
1
2
STORM
HYDRO
3
Add up the ordinates of all three to produce storm hydrograph
Multi-Period
Storm
• Pg - F = Net Rainfall
NET RF
UH
• RF units = UH duration
(i.e. 1 hour)
• Adjust UH by Net RF
• Add and Lag UH
• Produce Storm
Hydrograph
STORM
Development Effects on UH
Natural
Partial
Fully Developed
Synthetic UH
•Developed for basin that were ungaged
•Based on data from similar gaged basins
•Most methods are very similar in nature
•Revolutionized ability to predict hydro response
Synthetic UH Methods
•Methods to characterize
ungaged basins
•Use data and relationships
developed from gages
•Variety of approaches but
most based on Tp and Qp
•England and U.S. led the
efforts to standardize UH
Synthetic UH Methods
• Snyder’s Method (1938)
• Clark Method (1945)
• Nash (1958)
• SCS (1964, 1975)
• Espey-Winslow (1968)
• Kinematic Wave (1970s)
Snyder’s Method
 Synder (1938)- based on study of large
catchment in eastern US developed a set
of empirical equation for synthetic UH.
 The equation are use in USA and with
some modification in many other
countries.
Lag time
 The most important characteristic of
basin due to storm- basin lag (lag time)
 Lag time- time difference between the
centroid of the input (rainfall excess) and
the output (DRH)
 Represent time of travel of water from all
parts of watershed to the outlet during a
given storm.
Snyder’s Method
5 to 7 points
SCS Method
 Dimensionless UH
 Based on a study of large number of UH
 Developed by US Soil Conservation
Services (SCS)
SCS Methods
Triangular UH
Dimensionless UH
SCS Triangular UH Example
1 inch of RF over 1.6 hr duration
2-hr Duration UH Example
Qp at 400 cfs at 10 hr with 24 hr Tb
400
300
Six Hours of Uniform Rainfall = 0.25 in/hr
1.5 Inches Total Rain
200
100
2 4 6 8 10 12 14 16 18 20 22 24 26 30
Time in Hours
SCS RAINFALL RUNOFF CURVES
Unit Hydrograph Applications
Land Use 1
Land Use will alter
UH Peak and
Timing
Land Use 2
Unit Hydrograph Changes
Kinematic Wave
Overland
Collector
Channels
Main Stream
Manning’s Eqn
Kinematic Wave
Basin hydrographs- routed & combined
to produce storm hydrograph